A Comparison of I/O-Efficient Algorithms for Visibility Computation on Massive Grid Terrains

Herman Haverkort; Laura Toma

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arXiv · 1810.01946

A Comparison of I/O-Efficient Algorithms for Visibility Computation on Massive Grid Terrains

Herman Haverkort·Laura Toma

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Abstract

Given a grid terrain T and a viewpoint v, the viewshed of v is the set of grid points of T that are visible from v. To decide whether a point p is visible one needs to interpolate the elevation of the terrain along the line-of-sight vp. Existing viewshed algorithms differ widely in what points they chose to interpolate and how they interpolate the terrain. These choices crucially affect the running time and accuracy of the algorithms. This paper describes I/O-efficient algorithms for computing visibility maps in a couple of different models. First, we describe two algorithms that sweep the terrain by rotating a ray around the viewpoint while maintaining the terrain profile along the ray. Second, we describe an algorithm which sweeps the terrain centrifugally, growing a star-shaped region around the viewpoint while maintaining the approximate visible horizon of the terrain within the swept region. Our last two algorithms are based on computing and merging horizons. All algorithms are I/O-efficient in the I/O-model of Aggarwal and Vitter. We present an experimental analysis on large terrains obtained from NASA SRTM data. All our algorithms are scalable to volumes of data that are over 50 times larger than main memory. Our main finding is that, in practice, horizons are significantly smaller than their theoretical worst case bound, which makes horizon-based approaches very fast. Our last two algorithms, which compute the most accurate viewshed, turn out to be very fast in practice, although their worst-case bound is inferior.

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Herman Haverkort, Laura Toma. 2018-10-03. A Comparison of I/O-Efficient Algorithms for Visibility Computation on Massive Grid Terrains. https://arxiv.org/abs/1810.01946

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